Question

In the diagram, CE=12 units and BE=5 units.

Line l is a perpendicular bisector of line segment A C. It intersects line segment A C at point B. Line l also contains points D and E. Line segments A B and B C are the same length.

Based on the given information, what is AE?

2 units
7 units
12 units
17 units

Answer 1

Given : CE=12 units and BE=5

AB = BC

To Find : AE

2 units

7 units

12 units

17 units

Solution:

∠ABE  = ∠DBC = 90°   vertically opposite angles  

∠CBE =  180° - ∠ABE  = 90°

in Δ CBE  & ΔABE

∠CBE = ∠ABE = 90°

CB = AB  given

BE = BE  common

=> Δ CBE  ≅ ΔABE   (SAS)

=> CE = AE  

  => AE = 12    

AE = 12 unit

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